具有高阶差分算子的超阶共享有限集全函数的研究

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2302417g

Hong-Fang Guo, F. Lü, W. Lü

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引用次数: 0

摘要

本文利用Borel引理和Clunie引理，推导出一个超阶小于1的完整函数f与它的第n个差分算子?nc f (z)之间的关系，如果它们共享一个有限集，并且f有一个Borel例外值0，其中该集合由两个较小阶的完整函数组成。此外，还给出了f的精确形式，并举例说明了条件的尖锐性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A study on entire functions of hyper-order sharing a finite set with their high-order difference operators

In this paper, due to the Borel lemma and Clunie lemma, we will deduce the relationship between an entire function f of hyper-order less than 1 and its n-th difference operator ?nc f (z) if they share a finite set and f has a Borel exceptional value 0, where the set consists of two entire functions of smaller orders. Moreover, the exact form of f is given and an example is provided to show the sharpness of the condition.

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